Communication system and method of data communications

A communication system includes a transmitter configured to transmit a modulated signal, a transmission line configured to carry the modulated signal, and a receiver coupled to the transmitter by the transmission line, and configured to receive the modulated signal. The transmitter includes a modulator configured to generate the modulated signal responsive to a data signal and a carrier signal. The receiver includes a demodulator configured to demodulate the modulated signal responsive to a first carrier signal. The demodulator includes a filter and a gain adjusting circuit configured to adjust a gain of the filter, and to generate the set of control signals based on a voltage of the filtered first signal and a voltage of the first signal. The gain adjusting circuit includes a first peak detector coupled to the filter, and configured to detect a peak value of the voltage of the filtered first signal.